David Shulkin, the secretary of veterans affairs, during a cabinet meeting at the White House this month.Credit
Doug Mills/The New York Times

WASHINGTON — President Trump, fresh off replacing his secretary of state and C.I.A. director, is considering firing his secretary of veterans affairs and installing Energy Secretary Rick Perry in the post, according to two people close to the White House.

Mr. Trump did not make a formal offer to Mr. Perry when the two men met on Monday. But the people said the president has grown impatient with the department’s current secretary, Dr. David Shulkin, and may want to replace him with someone already in his cabinet.

It was unclear if Mr. Perry, who was an Air Force pilot before entering politics, would accept the change in position if Mr. Trump offered it, or if Mr. Trump had a successor in mind to lead the Energy Department.

The White House did not immediately respond to requests for comment, nor did Dr. Shulkin.

The conversation follows weeks of bitter infighting at the Veterans Affairs Department, where Dr. Shulkin has faced off in a rare public spat with a prominent group of Trump administration appointees who want to see him removed from office. The dispute goes beyond personality to a struggle over how far and how fast to privatize health care under the V.A. system.

A politically moderate former hospital executive who also served in the Obama administration, Dr. Shulkin had been one of Mr. Trump’s most popular cabinet secretaries, both in the White House and on Capitol Hill. At a time when Mr. Trump was struggling to find legislative victories, Dr. Shulkin and Congress’s veterans committees delivered a string of popular, bipartisan bills to the president’s desk.

And Mr. Trump has publicly showered Dr. Shulkin with praise. At a signing ceremony for one of those bills in June, Mr. Trump said his secretary did not have to worry about hearing the president’s old reality-show catchphrase, “You’re fired.”

“We’ll never have to use those words on our David,” Mr. Trump said, pointing his finger at the secretary like a pistol. “We will never use those words on you, that’s for sure.”

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That tenor began to change in recent months, as Dr. Shulkin increasingly butted heads with conservative Trump administration officials over one of the White House’s top policy priorities for the department: the expansion of government-subsidized private health care for veterans, outside the government-run V.A. health system.

The conservatives came to feel that Dr. Shulkin, who advocated a moderate rewrite of the current private care programs, was an obstacle to their goal.

The dispute spilled into public over the last month, following a scathing report by department’s inspector general on a business trip that Dr. Shulkin took to Britain and Denmark last year. The report found “serious derelictions” related to the trip and concluded that the secretary spent much of it sightseeing and improperly accepted a gift of Wimbledon tickets.

The report in hand, Dr. Shulkin’s critics in the White House and the department — including his two top communications deputies — worked behind the scenes to try to hasten his ouster. Dr. Shulkin, who disputed the report’s findings, went public with fears that appointees were “trying to undermine the department from within.” He iced out those he viewed as a threat and essentially became his own one-person press office.

As recently as last week, after a series of meetings with John F. Kelly, the White House chief of staff, Dr. Shulkin publicly declared victory, hinting that he had the White House’s support to remove officials battling him.

The secretary appeared to be regaining his footing. He sat at Mr. Trump’s side during a cabinet meeting, and the two men together called Senator Johnny Isakson of Georgia, the chairman of the Veterans’ Affairs Committee, to pledge their support for his more moderate health care legislation, according to a congressional aide briefed on the call. The secretary maintains the support of top Democrats and Republicans on Capitol Hill.

But top White House officials have only become more irked with the secretary’s penchant for publicly discussing internal politics, and Mr. Trump has begun searching for a replacement.

Mr. Perry is seen as a more pliant figure for the veterans affairs position. Unlike Dr. Shulkin, who had run the department’s health care system under President Barack Obama and spent a career in hospital administration, Mr. Perry has no background in health care delivery, but as Texas’ governor, he showed a willingness to experiment.

If Mr. Trump were to make the move, possible replacements for Mr. Perry could include Ray Washburne, a Dallas entrepreneur and prominent Republican fund-raiser; J. Larry Nichols, the former chairman of Devon Energy; and T. Boone Pickens, the Texas oilman, according to people who work closely with senior officials at the department and the White House.

A version of this article appears in print on March 14, 2018, on Page A12 of the New York edition with the headline: Veterans Affairs Secretary May Be Next One Ousted. Order Reprints|Today's Paper|Subscribe